Metropolitan and peripheral theories about Britain's involvement in the Scramble for Africa don't really compete with one another, as your question suggests. In fact, peripheral theories attempt to model the outcomes of colonialism, not its causes. Metropolitan theories model the causes of imperialism, not its effects.
The Scramble for Africa was a name given to the efforts by European powers to establish colonial outposts in Africa in the second half of the Nineteenth Century. At the time, this wasn't recognized as a single effort or period of history. That name was applied later. See Thomas Pakenham's very good history of the period, The Scramble for Africa.
In the case of Britain's imperialism in Africa, there were three main factors involved. The first and most important was competition with other great powers in Europe. The Berlin Conference of 1885 was an agreement between Belgium, Britain, France and Germany to peaceably divide the African continent into spheres of influence, to prevent war between them over competition for land and resources.
Once spheres of influence had been settled, Britain (like the other European powers involved) could safely increase trade, encourage European settlement and further develop extraction industries or cash crop economies in its protectorates. These lands also gave Britain markets for its exports, particularly finished cloth, small manufactures like pottery and metal tools, and guns.
Sometimes leading and sometimes following this expansion of economic activity, explorers and missionaries penetrated African lands hitherto unknown to Europeans. These efforts were undertaken for their own sake, but they functioned as proxies for the military (mapping and claiming new territory) and colonial governments (winning "souls" for the British way of life and its churches).
Theoretical treatments of these trends which fit under the heading Metropolitan Theory are exemplified in Harold Innis' ideas about the center and the periphery. Historians like PT Bauer, Robert Bates, and Walter Rodney have used similar ideas to explain how Britain "opened" Africa, though they do so from unrelated perspectives.
Periphery theories about the effects of British colonialism are usually gathered under a rubric called Dependency Theory. Three of the best authors you can read on these topics are Samir Amin, Immanuel Wallerstein, and Guillermo O'Donnell.
Edward Said's excellent book, Culture and Imperialism, investigates these questions thoroughly and well. I highly recommend it.